As this type of vibration-damping device, for example, a device shown in the following Patent Document 1 is known. This device includes an outer tube which is connected to one of a vibration generating portion and a vibration receiving portion, an attaching member which is connected to the other of the vibration generating portion and the vibration receiving portion, and is arranged on the inner circumferential side of the outer tube, a first rubber elastic body which elastically connects the outer tube and the attaching member together, and closes an opening at a first end of the outer tube in the direction of an axis, a diaphragm which closes an opening at a second end in which the other end of the outer tube in the direction of the axis, and a partition member which elastic body at a portion of a partition wall, and an auxiliary fluid chamber having the diaphragm at a portion of the partition wall. Additionally, an orifice passage which allows the main fluid chamber and the auxiliary fluid chamber to communicate with each other is formed between the outer circumferential surface of the partition member and the inner circumferential surface of the outer tube.    [Patent Document 1] JP-A-8-291835